Abstract
Packing 3D objects into a known container is a very common task in many industries such as packaging, transportation, and manufacturing. This important problem is known to be NP-hard and even approximate solutions are challenging. This is due to the difficulty of handling interactions between objects with arbitrary 3D geometries and a vast combinatorial search space. Moreover, the packing must be interlocking-free for real-world applications. In this work, we first introduce a novel packing algorithm to search for placement locations given an object. Our method leverages a discrete voxel representation. We formulate collisions between objects as correlations of functions computed efficiently using Fast Fourier Transform (FFT). To determine the best placements, we utilize a novel cost function, which is also computed efficiently using FFT. Finally, we show how interlocking detection and correction can be addressed in the same framework resulting in interlocking-free packing. We propose a challenging benchmark with thousands of 3D objects to evaluate our algorithm. Our method demonstrates state-of-the-art performance on the benchmark when compared to existing methods in both density and speed.
Supplemental Material
Available for Download
supplemental material
- Luiz JP Araújo, Ender Özcan, Jason AD Atkin, and Martin Baumers. 2019. Analysis of irregular three-dimensional packing problems in additive manufacturing: a new taxonomy and dataset. International Journal of Production Research 57, 18 (2019), 5920--5934.Google ScholarCross Ref
- Richard Carl Art Jr. 1966. An approach to the two dimensional irregular cutting stock problem. Ph.D. Dissertation. Massachusetts Institute of Technology.Google Scholar
- Autodesk. 2023. Autodesk Netfabb. https://www.autodesk.com/products/netfabb/ Build: 47, Release: 2023.1.Google Scholar
- Edmund K Burke, Robert SR Hellier, Graham Kendall, and Glenn Whitwell. 2007. Complete and robust no-fit polygon generation for the irregular stock cutting problem. European Journal of Operational Research 179, 1 (2007), 27--49.Google ScholarCross Ref
- Elizabeth R Chen, Michael Engel, and Sharon C Glotzer. 2010. Dense crystalline dimer packings of regular tetrahedra. Discrete & Computational Geometry 44, 2 (2010), 253--280.Google ScholarDigital Library
- Rulin Chen, Ziqi Wang, Peng Song, and Bernd Bickel. 2022. Computational design of high-level interlocking puzzles. ACM Trans. Graph. 41, 4 (2022), 1--15.Google ScholarDigital Library
- Xuelin Chen, Hao Zhang, Jinjie Lin, Ruizhen Hu, Lin Lu, Qi-Xing Huang, Bedrich Benes, Daniel Cohen-Or, and Baoquan Chen. 2015. Dapper: decompose-and-pack for 3d printing. ACM Trans. Graph. 34, 6 (2015), 213--1.Google ScholarDigital Library
- Nikolai Chernov, Yuriy Stoyan, and Tatiana Romanova. 2010. Mathematical model and efficient algorithms for object packing problem. Computational Geometry 43, 5 (2010), 535--553.Google ScholarDigital Library
- Erwin Coumans and Yunfei Bai. 2016--2021. PyBullet, a Python module for physics simulation for games, robotics and machine learning. http://pybullet.org.Google Scholar
- Jens Egeblad, Claudio Garavelli, Stefano Lisi, and David Pisinger. 2010. Heuristics for container loading of furniture. European Journal of Operational Research 200, 3 (2010), 881--892.Google ScholarCross Ref
- Christer Ericson. 2004. Real-time collision detection. Crc Press.Google Scholar
- Filippo Andrea Fanni, Fabio Pellacini, Riccardo Scateni, and Andrea Giachetti. 2022. PAVEL: Decorative Patterns with Packed Volumetric Elements. ACM Transactions on Graphics (TOG) 41, 2 (2022), 1--15.Google ScholarDigital Library
- Michael Fogleman. 2019. Pack3d. https://github.com/fogleman/pack3dGoogle Scholar
- Michael Garland and Paul S Heckbert. 1997. Surface simplification using quadric error metrics. In Proceedings of the 24th annual conference on Computer graphics and interactive techniques. 209--216.Google ScholarDigital Library
- Michael Goldwasser, J-C Latombe, and Rajeev Motwani. 1996. Complexity measures for assembly sequences. In Proceedings of IEEE International Conference on Robotics and Automation, Vol. 2. IEEE, 1851--1857.Google ScholarCross Ref
- Ankit Goyal and Jia Deng. 2020. PackIt: A Virtual Environment for Geometric Planning. In International Conference on Machine Learning.Google Scholar
- Si Hang. 2015. TetGen, a Delaunay-based quality tetrahedral mesh generator. ACM Trans. Math. Softw 41, 2 (2015), 11.Google Scholar
- Ruizhen Hu, Juzhan Xu, Bin Chen, Minglun Gong, Hao Zhang, and Hui Huang. 2020. TAP-Net: transport-and-pack using reinforcement learning. ACM Trans. Graph. 39, 6 (2020), 1--15.Google ScholarDigital Library
- Alec Jacobson, Daniele Panozzo, et al. 2018. libigl: A simple C++ geometry processing library. https://libigl.github.io/.Google Scholar
- David S Johnson. 1973. Near-optimal bin packing algorithms. Ph. D. Dissertation. Massachusetts Institute of Technology.Google Scholar
- Ephraim Katchalski-Katzir, Isaac Shariv, Miriam Eisenstein, Asher A Friesem, Claude Aflalo, and Ilya A Vakser. 1992. Molecular surface recognition: determination of geometric fit between proteins and their ligands by correlation techniques. Proc Natl Acad of Sci 89, 6, 2195--2199.Google ScholarCross Ref
- Carlos Lamas-Fernandez, Julia A Bennell, and Antonio Martinez-Sykora. 2022. Voxel-Based Solution Approaches to the Three-Dimensional Irregular Packing Problem. Operations Research (2022).Google Scholar
- Lei Lan, Danny M Kaufman, Minchen Li, Chenfanfu Jiang, and Yin Yang. 2022. Affine body dynamics: Fast, stable & intersection-free simulation of stiff materials. arXiv preprint arXiv:2201.10022 (2022).Google Scholar
- Steven M LaValle. 2006. Planning algorithms. Cambridge university press.Google ScholarDigital Library
- Aline AS Leao, Franklina MB Toledo, José Fernando Oliveira, Maria Antónia Carravilla, and Ramón Alvarez-Valdés. 2020. Irregular packing problems: A review of mathematical models. European Journal of Operational Research 282, 3 (2020), 803--822.Google ScholarCross Ref
- Xiao Liu, Jia-min Liu, An-xi Cao, and Zhuang-le Yao. 2015. HAPE3D---a new constructive algorithm for the 3D irregular packing problem. Frontiers of Information Technology & Electronic Engineering 16, 5 (2015), 380--390.Google ScholarCross Ref
- Yuexin Ma, Zhonggui Chen, Wenchao Hu, and Wenping Wang. 2018. Packing irregular objects in 3D space via hybrid optimization. Comp. Graph. Forum (SGP) 37, 5 (2018), 49--59.Google ScholarCross Ref
- Silvano Martello, David Pisinger, and Daniele Vigo. 2000. The three-dimensional bin packing problem. Operations research 48, 2 (2000), 256--267.Google Scholar
- NVIDIA. 2022a. CUDA, release: 12.0. https://developer.nvidia.com/cuda-toolkitGoogle Scholar
- NVIDIA. 2022b. CUDA, release: 12.0. https://developer.nvidia.com/cufftGoogle Scholar
- Dzmitry Padhorny, Andrey Kazennov, Brandon S Zerbe, Kathryn A Porter, Bing Xia, Scott E Mottarella, Yaroslav Kholodov, David W Ritchie, Sandor Vajda, and Dima Kozakov. 2016. Protein-protein docking by fast generalized Fourier transforms on 5D rotational manifolds. Proc Natl Acad Sci 113, 30, E4286--E4293.Google ScholarCross Ref
- Alexander Pankratov, Tatiana Romanova, and Igor Litvinchev. 2020. Packing oblique 3D objects. Mathematics 8, 7 (2020), 1130.Google ScholarCross Ref
- Bernhard Reinert, Tobias Ritschel, and Hans-Peter Seidel. 2013. Interactive by-example design of artistic packing layouts. ACM Transactions on Graphics (TOG) 32, 6 (2013), 1--7.Google ScholarDigital Library
- David W Ritchie and Graham JL Kemp. 2000. Protein docking using spherical polar Fourier correlations. Proteins: Structure, Function, and Bioinformatics 39, 2 (2000), 178--194.Google ScholarCross Ref
- David W Ritchie and Vishwesh Venkatraman. 2010. Ultra-fast FFT protein docking on graphics processors. Bioinformatics 26, 19 (2010), 2398--2405.Google ScholarDigital Library
- Tatiana Romanova, Julia Bennell, Yuriy Stoyan, and Aleksandr Pankratov. 2018. Packing of concave polyhedra with continuous rotations using nonlinear optimisation. European Journal of Operational Research 268, 1 (2018), 37--53.Google ScholarCross Ref
- Michael Schwarz and Hans-Peter Seidel. 2010. Fast parallel surface and solid voxelization on GPUs. ACM transactions on graphics (TOG) 29, 6 (2010), 1--10.Google Scholar
- Sculpteo. 2023. Sculpteo Fabpilot. https://www.fabpilot.com/.Google Scholar
- Pitchaya Sitthi-Amorn, Javier E Ramos, Yuwang Wangy, Joyce Kwan, Justin Lan, Wenshou Wang, and Wojciech Matusik. 2015. MultiFab: a machine vision assisted platform for multi-material 3D printing. Acm Transactions on Graphics (Tog) 34, 4 (2015), 1--11.Google ScholarDigital Library
- Peng Song, Chi-Wing Fu, and Daniel Cohen-Or. 2012. Recursive interlocking puzzles. ACM Trans. Graph. 31, 6 (2012), 1--10.Google ScholarDigital Library
- Yuriy Stoyan, Aleksandr Pankratov, and Tatiana Romanova. 2016. Quasi-phi-functions and optimal packing of ellipses. Journal of Global Optimization 65, 2 (2016), 283--307.Google ScholarDigital Library
- Yunsheng Tian, Jie Xu, Yichen Li, Jieliang Luo, Shinjiro Sueda, Hui Li, Karl DD Willis, and Wojciech Matusik. 2022. Assemble Them All: Physics-Based Planning for Generalizable Assembly by Disassembly. ACM Transactions on Graphics (TOG) 41, 6 (2022), 1--11.Google ScholarDigital Library
- UnionTech. 2018. Polydevs. https://polydevs3d.com/ Version 2.2.5.33.Google Scholar
- Juraj Vanek, JA Garcia Galicia, Bedrich Benes, R Měch, N Carr, Ondrej Stava, and GS Miller. 2014. Packmerger: A 3d print volume optimizer. In Computer Graphics Forum, Vol. 33. Wiley Online Library, 322--332.Google Scholar
- Fan Wang and Kris Hauser. 2019. Stable bin packing of non-convex 3D objects with a robot manipulator. In 2019 International Conference on Robotics and Automation (ICRA). IEEE, 8698--8704.Google ScholarDigital Library
- Ziqi Wang, Peng Song, and Mark Pauly. 2018. DESIA: A general framework for designing interlocking assemblies. ACM Transactions on Graphics (TOG) 37, 6 (2018), 1--14.Google ScholarDigital Library
- Ziqi Wang, Peng Song, and Mark Pauly. 2021. State of the Art on Computational Design of Assemblies with Rigid Parts. Eurographics 2021 STAR 40 (2021).Google Scholar
- Randall H Wilson and Jean-Claude Latombe. 1994. Geometric reasoning about mechanical assembly. Artificial Intelligence 71, 2 (1994), 371--396.Google ScholarDigital Library
- Zifei Yang, Shuo Yang, Shuai Song, Wei Zhang, Ran Song, Jiyu Cheng, and Yibin Li. 2021. PackerBot: Variable-Sized Product Packing with Heuristic Deep Reinforcement Learning. In 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 5002--5008.Google Scholar
- Miaojun Yao, Zhili Chen, Linjie Luo, Rui Wang, and Huamin Wang. 2015. Level-set-based partitioning and packing optimization of a printable model. ACM Transactions on Graphics (TOG) 34, 6 (2015), 1--11.Google ScholarDigital Library
- Cha Zhang and Tsuhan Chen. 2001. Efficient feature extraction for 2D/3D objects in mesh representation. In Proceedings 2001 International Conference on Image Processing (Cat. No. 01CH37205), Vol. 3. IEEE, 935--938.Google ScholarCross Ref
- Xinya Zhang, Robert Belfer, Paul G Kry, and Etienne Vouga. 2020. C-Space tunnel discovery for puzzle path planning. ACM Transactions on Graphics (TOG) 39, 4 (2020), 104--1.Google ScholarDigital Library
- Hongkai Zhao. 2005. A fast sweeping method for eikonal equations. Mathematics of computation 74, 250 (2005), 603--627.Google Scholar
- Hang Zhao, Qijin She, Chenyang Zhu, Yin Yang, and Kai Xu. 2021. Online 3D bin packing with constrained deep reinforcement learning. In Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 35. 741--749.Google ScholarCross Ref
- Qingnan Zhou and Alec Jacobson. 2016. Thingi10k: A dataset of 10,000 3d-printing models. arXiv preprint arXiv:1605.04797 (2016).Google Scholar
Index Terms
- Dense, Interlocking-Free and Scalable Spectral Packing of Generic 3D Objects
Recommendations
A two-stage tabu search algorithm with enhanced packing heuristics for the 3L-CVRP and M3L-CVRP
The Three-Dimensional Loading Capacitated Vehicle Routing Problem (3L-CVRP) addresses practical constraints frequently encountered in the freight transportation industry. In this problem, the task is to serve all customers using a homogeneous fleet of ...
Strip Packing vs. Bin Packing
AAIM '07: Proceedings of the 3rd international conference on Algorithmic Aspects in Information and ManagementIn this paper we establish a general algorithmic framework between bin packing and strip packing, with which we achieve the same asymptotic bounds by applying bin packing algorithms to strip packing. More precisely we obtain the following results: (1) ...
A Harmonic Algorithm for the 3D Strip Packing Problem
In the three-dimensional (3D) strip packing problem, we are given a set of 3D rectangular items and a 3D box $B$. The goal is to pack all the items in $B$ such that the height of the packing is minimized. We consider the most basic version of the problem, ...
Comments